Frog -in -the -Box codes and robust quantization.

Abstract

The design of robust quantizers that are insensitive to channel noise has been a prominent problem in joint source-channel coding. In this thesis, a simple design strategy for robust quantizers with good performance is presented. The strategy is based on the use of a new class of ordered binary codes called Frog-in-the-Box codes, which are generalizations of Snake-in-the-Box codes. Frog-in-the-Box codes are designed so that their codeword ordering and inter-codeword Hamming distances make them ideal for use as index assignments for the robust quantizer. More specifically, Frog-in-the-Box codes have a limited distance-preserving property where the Hamming distance between any two codewords is proportional to their separation in the codeword ordering. In this thesis, Frog-in-the-Box codes are defined and basic properties of these codes are established. Bounds on the largest possible Frog-in-the-Box codes are found, and an efficient code construction algorithm is developed. This algorithm has enabled the creation of a large library of Frog-in-the-Box codes. The large selection of Frog-in-the-Box codes found in this thesis allowed for extensive research into their performance as robust quantizer index assignments. The use of Frog-in-the-Box codes simplifies the usual index assignment design process. Moreover, the resulting index assignments have good performance compared to other index assignment strategies, and work well regardless of the source or channel. In short, Frog-in-the-Box code index assignments enable a simple and universal method of designing robust quantizers.